PART B

4. (10 points) A machine has the first cost of $60K. The net annual savings (which depends on the volume of throughput) and the salvage value at the end of its 8-year economic life (which depends on the progress in related technology) are given below: Volume of throughput High Medium Low Probability 0.3 0.6 0.1 Annual Savings AS $30K $20K $10K Rate of technological progress Incremental Revolutionary 0.75 0.25 $9K $3K Probability Salvage S Assume that the progress in technology and the level of throughput volume are independent, and MARR is 10% a) Write the probability distribution of EAW, then compute the expected EAW, the standard deviation of EAW and the probability the there will be a loss in this investment. You may first write down the following formula: EAW(10%) =......-60,000l Ajp, 10% 6)+ AS + S (ALF 10% 6). Then fill in the following table: (Note: (A/P, 10%, 8) = 0.1874; (A/F, 10%, 8) = 0.0874) 30 Prob EAW_ 4,397 1426 4294 1353 Combination: AS (SK) S(SK) Prob E AW(S) 0.225 19,543 30 0.075 19018 20 9 45 9543 20 0.15 9,018 109 0.075 - 457 103 0.025 -982 Sum: E(EAM = $11,412 SD(EAW) = $12.995 Prob*EAW2 85,304,473 27,126895 40,977,547 12,199,190 15,691 24,098 164,273894 11,412 b) Is this a good investment based on your own return/risk trade-off? Why or why not? If the distribution of PW is approximately normal, what is the probability of loss? (Table of Standard Normal distribution is given.) 0.3 STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 50000 50399 30798 51197 51595 519945239252790 53188 53586 53983 5438054776 5517255567 5596256356 5674957142 57535 57926 58317 58706 59095 594835987160257 60642 61026 61409 26179162172 6255262930 633076368364058644316480365173 0.4 .65542 .65910 66276 666-10 6700367364 677246808268439 .68793 0.5 .69146 69497 69847 70194 70540 70884 712267 1566 71904 72240 0. 6 7257572907 73237 73565 7389174215 74537 74857 75175 75.490 0.7 .75804 76115 .76424 .76730 77035 77337 77637 .77935 .78230 .78524 .78814 79103 79389 179673 79955 .80234 80511 80785 81057 81327 .81594 .81859 .82121 82381 82639 82894 83147 .83398 83646 .83891 .84134 84375 84614 848498508385314 85543 8576985993 86214 .86433 .86650 .86864 .87076 87286 87493 87698 .87900 .88100 188298 88493 .88686 88877 .89065 89251 89435 89617 .89796 8997390147 90320 90490 90658 90824 90988 9114991309 91466 91621 91774 91924 92073 9222092364 92507 92647 92785 92922 93056 93189 .93319 93448 93574 93699 93822 93943 94062 .94179 94295 94408 945209463094738 9484594950 95053 95154 95254 95352 95449 95543 95637 95728 95818 95907 95994 96080 96164 96246 96327 96407964859656296638 96712 96784 9685696926 9699597062 97128 97193 97257 97320 97381 97381 97441 97500 97558 97615 97670 2.0 97725 97778 97831 97882 97932 97982 98030 98077 98124 98169 98214 98257 .98300 98341 98382 98422 98461 98500 98537 98574 98610 98645 .98679 98713 98745 98778 98809 98840 98870 98899 98928 98956 98983 .9901099036 99061 99086 99111 99134 99158 99180 9920299224 99245 99266 99286 99305 99324 99343 99361 99379 99396 99413 99430 99446 99461 99477 99492 99506 99520 2.6 99534 .99547 99560 99573 99585 99598 99609 99621 99632 99643 99653 99661 99674 99683 99693 9970299711 99720 99728 99736 99744 99732 99760 997679977499781 99788 9979599801 99807 2. 9 998139981999825 99831 99836 9984199846 99851 99856 99861 .99865 9986999874 99878 99882 99886 9988999893 99896 .99900 199903 99906 99910 99913 9991699918 999219992499926 99929 9993199934 99936 99938 99940 99942 99944 99946 99948 99950 9995299953 99955 9995799958 99960 99961 99962 99964 99965 -99966 99968 9996999970999719997299973 .99974 99975 .99976 99977 99978 99978 99979 99980 99981 99981 99982 99983 99983 99984 99985 99985 99986 99986 9998799987 99988 99988 99989 99989 .99990 99990 99990 9999199991 99992 99992 99992 .99992 99993999939999399994 9999499994 99994 99995 99995 99995 3.9 999999999999996 99996 99996 999969999699996 9999799997 2.4 2.7 3.0 3.2 3.3 3.4 3.5 3.7 3.8 4. (10 points) A machine has the first cost of $60K. The net annual savings (which depends on the volume of throughput) and the salvage value at the end of its 8-year economic life (which depends on the progress in related technology) are given below: Volume of throughput High Medium Low Probability 0.3 0.6 0.1 Annual Savings AS $30K $20K $10K Rate of technological progress Incremental Revolutionary 0.75 0.25 $9K $3K Probability Salvage S Assume that the progress in technology and the level of throughput volume are independent, and MARR is 10% a) Write the probability distribution of EAW, then compute the expected EAW, the standard deviation of EAW and the probability the there will be a loss in this investment. You may first write down the following formula: EAW(10%) =......-60,000l Ajp, 10% 6)+ AS + S (ALF 10% 6). Then fill in the following table: (Note: (A/P, 10%, 8) = 0.1874; (A/F, 10%, 8) = 0.0874) 30 Prob EAW_ 4,397 1426 4294 1353 Combination: AS (SK) S(SK) Prob E AW(S) 0.225 19,543 30 0.075 19018 20 9 45 9543 20 0.15 9,018 109 0.075 - 457 103 0.025 -982 Sum: E(EAM = $11,412 SD(EAW) = $12.995 Prob*EAW2 85,304,473 27,126895 40,977,547 12,199,190 15,691 24,098 164,273894 11,412 b) Is this a good investment based on your own return/risk trade-off? Why or why not? If the distribution of PW is approximately normal, what is the probability of loss? (Table of Standard Normal distribution is given.) 0.3 STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 50000 50399 30798 51197 51595 519945239252790 53188 53586 53983 5438054776 5517255567 5596256356 5674957142 57535 57926 58317 58706 59095 594835987160257 60642 61026 61409 26179162172 6255262930 633076368364058644316480365173 0.4 .65542 .65910 66276 666-10 6700367364 677246808268439 .68793 0.5 .69146 69497 69847 70194 70540 70884 712267 1566 71904 72240 0. 6 7257572907 73237 73565 7389174215 74537 74857 75175 75.490 0.7 .75804 76115 .76424 .76730 77035 77337 77637 .77935 .78230 .78524 .78814 79103 79389 179673 79955 .80234 80511 80785 81057 81327 .81594 .81859 .82121 82381 82639 82894 83147 .83398 83646 .83891 .84134 84375 84614 848498508385314 85543 8576985993 86214 .86433 .86650 .86864 .87076 87286 87493 87698 .87900 .88100 188298 88493 .88686 88877 .89065 89251 89435 89617 .89796 8997390147 90320 90490 90658 90824 90988 9114991309 91466 91621 91774 91924 92073 9222092364 92507 92647 92785 92922 93056 93189 .93319 93448 93574 93699 93822 93943 94062 .94179 94295 94408 945209463094738 9484594950 95053 95154 95254 95352 95449 95543 95637 95728 95818 95907 95994 96080 96164 96246 96327 96407964859656296638 96712 96784 9685696926 9699597062 97128 97193 97257 97320 97381 97381 97441 97500 97558 97615 97670 2.0 97725 97778 97831 97882 97932 97982 98030 98077 98124 98169 98214 98257 .98300 98341 98382 98422 98461 98500 98537 98574 98610 98645 .98679 98713 98745 98778 98809 98840 98870 98899 98928 98956 98983 .9901099036 99061 99086 99111 99134 99158 99180 9920299224 99245 99266 99286 99305 99324 99343 99361 99379 99396 99413 99430 99446 99461 99477 99492 99506 99520 2.6 99534 .99547 99560 99573 99585 99598 99609 99621 99632 99643 99653 99661 99674 99683 99693 9970299711 99720 99728 99736 99744 99732 99760 997679977499781 99788 9979599801 99807 2. 9 998139981999825 99831 99836 9984199846 99851 99856 99861 .99865 9986999874 99878 99882 99886 9988999893 99896 .99900 199903 99906 99910 99913 9991699918 999219992499926 99929 9993199934 99936 99938 99940 99942 99944 99946 99948 99950 9995299953 99955 9995799958 99960 99961 99962 99964 99965 -99966 99968 9996999970999719997299973 .99974 99975 .99976 99977 99978 99978 99979 99980 99981 99981 99982 99983 99983 99984 99985 99985 99986 99986 9998799987 99988 99988 99989 99989 .99990 99990 99990 9999199991 99992 99992 99992 .99992 99993999939999399994 9999499994 99994 99995 99995 99995 3.9 999999999999996 99996 99996 999969999699996 9999799997 2.4 2.7 3.0 3.2 3.3 3.4 3.5 3.7 3.8